In recent years, fine particles such as dust and mist suspended in gaseous atmosphere have been receiving attention, in association with suppression of particle contamination in a semiconductor manufacturing process, development of quantum nanoscale material, clarification of generating mechanism of acid rain and smog in the air, and so on.
Differential mobility analyzers (DMAs) have been used to classify aerosol particles that are of nanometer-scale to micrometer-scale particle size. The DMAs make use of a phenomenon that electrical mobility of charged particles in airflow is dependent on their particle size. Cylindrical differential mobility analyzers (CDMAs) are widely used among the DMAs (see Non Patent Literature 1). As a result of significant progress in the recent years, the DMAs are now capable of classifying charged particles having such minimal particle size as 10 nanometers or less at the smallest, and are operable even under reduced pressure (see Patent Literature 1).
FIG. 9 illustrates an example of a conventional CDMA. As illustrated in FIG. 9, a CDMA 800 has a double cylinder structure including a central rod (inner cylinder) 1 and a surrounding body (outer cylinder) 2. A predetermined voltage is applied between an inner peripheral surface of the surrounding body 2 (outer cylinder electrode) and an outer peripheral surface of the central rod 1 (inner cylinder electrode) by a variable voltage generator. Sheath gas is supplied from a supply opening (not illustrated) provided above the surrounding body 2 so as to form a laminar flow in a space between the surrounding body 2 and the central rod 1. The surrounding body 2 has an annular inlet slit 3 in its upper part, from which the charged particles are introduced into the analyzer. The central rod 1 has an annular outlet slit 4 in its lower part, from which the charged particles having been classified are discharged outside the analyzer.
The following description deals with a principle of classifying particles in the CDMA 800. Assume that, in the CDMA 800, a laminar flow condition of the sheath gas is not effected by sample gas containing the charged particles while the sample gas containing the charged particles is introduced via the inlet slit 3 at a predetermined flow rate Qa and discharged from the outlet slit 4 at the same flow rate Qa with respect to a sufficient flow rate of the sheath gas. The charged aerosol particles (charged particles), once entered via the inlet slit 3 into the analyzer, travels downwards in a central axis direction along the inner wall of the surrounding body 2, together with the sheath gas forming the laminar flow in the space between the surrounding body 2 and the central rod 1. Meanwhile, due to an effect caused by an electric field (electrostatic attraction) generated by the variable voltage generator between the surrounding body 2 and the central rod 1, just the aerosol particles of one polarity are attracted toward the central rod 1 at velocities corresponding to their electrical mobility. The electrical mobility is dependent on the particle size of each particle. On this account, just the aerosol particles having a particular particle size reach the outlet slit 4 and are discharged outside the analyzer via the outlet slit 4.
The electrical mobility Zp of the charged particle is calculated by the following equation (1):Zp=Qs·ln(R2/R1)/(2·π·V·L)  (1)In the equation (1), Qs is a flow rate of the sheath gas, R2 is a radius of the surrounding body 2, and R1 is a radius of the central rod 1, as illustrated in FIG. 9. L is a distance between the inlet slit 3 and the outlet slit 4 along a direction parallel to the central axis. V is the voltage applied between the inner peripheral surface of the surrounding body 2 and the outer peripheral surface of the central rod 1.
The electrical mobility Zp of the charged particle can also be calculated by the following equation (2):Zp=q·e·Cc/(3·π·μ·Dp)  (2)In the equation (2), q is a charge amount of the charged particle, e is an elementary electric charge, Cc is a Cunningham correction factor, μ is a coefficient of viscosity of the sheath gas, and Dp is a particle diameter of the charged particle.
By solving the equations (1) and (2) simultaneously, the following equation (3) is achieved:Dp=(2·V·L·q·e·Cc)/(3·μ·Qs·ln(R2/R1))  (3)It is understood from the equation (3) that the particle diameter Dp of the charged particle to be classified is calculated as a function of the applied voltage V.